Study of Aerodynamic Grain Entrainmentin Aeolian TransportG. Li1,2 , J. Zhang1, H. J. Herrmann3,4, Y. Shao5, and N. Huang1

1Key Laboratory of Mechanics on Disaster and Environment in Western China, Lanzhou University, Lanzhou, China,2School of Architecture, Civil, and Environmental Engineering, Swiss Federal Institute of Technology, Lausanne,Switzerland, 3PMMH, ESPCI, Paris, France, 4Department de Fisica, UFC, Fortaleza, Brazil, 5Institute for Geophysics andMeteorology, University of Cologne, Cologne, Germany

Abstract Aeolian transport controls landform formations on Earth and other planets and cruciallyaffects the atmospheric system. With elaborate wind tunnel measurements, we find that theaerodynamic entrainment rate follows a yet unreported exponential increase in the intermittent regimeand only complies with the expected linear law for the condition of continuous entrainment.Subsequently, we propose a model accounting for the effects of turbulence on aerodynamic entrainmentbased on the distribution of local shear stress to describe the experimental results. We also provideevidence that aerodynamic entrainment can be an efficient way to directly induce a horizontal graintransport comparable to the steady and saturated saltation in unsaturated conditions and should not beignored. Our findings substantially modify the present interpretation of surface erosion and bear thusimportant consequences on future soil protection techniques.

Plain Language Summary It has been recognized that grains can be lifted from the surfacethrough two mechanisms, either ejection due to the impact of grains in saltation or the pull‐out of grainsdue to aerodynamic entrainment. However, saltation has always been believed to be the dominantmechanism of aeolian sand transport. With elaborate wind tunnel measurements, we find that theaerodynamic entrainment rate follows a yet unreported exponential increase in the intermittent regime andonly complies with the expected linear law above the threshold to continuous flow. We also present the firstevidence that in fact turbulent grain entrainment contributes as least as much to or even more than theparticle flux in the continuous flow regime. Our discovery will open a new avenue of research focusing onaerodynamic grain entrainment and thus significantly influence the research of others. It also represents anessential step toward mastering soil erosion.

1. Introduction

Aeolian transport is common on several planetary bodies in the Solar System, such as Earth, Venus, Mars,and Titan (Lorenz & Zimbelman, 2014), inducing a large shape variety of planetary landforms. It has greatinfluence on the atmospheric system through the emission of airborne dust grains (Kok et al., 2012). It is alsoresponsible for desertification and dune formation and thus of considerable importance to environmentalstudies (Shao, 2008).

It has been recognized that grains can be lifted from the surface through two mechanisms, either ejectiondue to the impact of grains in saltation or the pull‐out of grains due to aerodynamic entrainment(Bagnold, 1941). Saltation impact is widely recognized as themechanism sustaining wind‐blown grain trans-port and has been extensively investigated in the past decades (Anderson &Haff, 1988; Bagnold, 1941; Kok etal., 2012; Owen, 1964; Shao & Li, 1999). However, only a few studies (Anderson & Haff, 1988; Doorschot &Lehning, 2002; Shao & Li, 1999; Williams et al., 1990, 1994) have tried to quantify aerodynamic entrainmentwhich is normally considered as an inception of saltation and to be negligible in the stationary state of salta-tion (Bagnold, 1941; Kok et al., 2012), although some new evidences (Baker et al., 2018; Klose et al., 2015;Pähtz et al., 2018; Sullivan &Kok, 2017; Zhang et al., 2016) show that aerodynamic entrainment is importantand can even play a dominant role in some places where saltation is limited or special atmospheric condi-tions are encountered, as is it the case on Mars.

©2020. American Geophysical Union.All Rights Reserved.This is an open access article under theterms of the Creative CommonsAttribution License, which permits use,distribution and reproduction in anymedium, provided the original work isproperly cited.

RESEARCH LETTER10.1029/2019GL086574

Key Points:• Two scaling laws are found between

aerodynamic entrainment rate ofgrains and mean surface shear stressin wind tunnel experiments

• A predictive model consideringturbulence is proposed to explain theaerodynamic entrainment rate

• Aerodynamic entrainment is able tocause streamwise grain flux inunsaturated sand stream

Supporting Information:• Supporting Information S1• Table S1

Correspondence to:J. Zhang and N. Huang,huangn@lzu.edu.cn;zhang-j@lzu.edu.cn

Citation:Li, G., Zhang, J., Herrmann, H. J., Shao,Y., & Huang, N.. (2020). Study ofaerodynamic grain entrainment inaeolian transport. Geophysical ResearchLetters, 47, e2019GL086574. https://doi.org/10.1029/2019GL086574

Received 6 DEC 2019Accepted 23 FEB 2020Accepted article online 29 APR 2020

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The amount of particles entrained directly by wind can be physically described by horizontal momentumconservation as

ΔmÄnup¼ τs − τtð ÞÄnΔtÄnA (1)

where Δm is the mass of particles emitted from the surface with a typical horizontal escape velocity up. τsis the wind shear stress exerted on the surface and τt the critical shear stress to initiate particle motion (i.e.,aerodynamic threshold, which is depended on the constraining force of exposed particles). Δt and A are,respectively, the duration and surface area of the measurement.

The following law can be derived from equation 1:

F¼α τs − τtð Þ (2)

where F = Δm/(Δt · A) is defined as aerodynamic entrainment rate and α = 1/up is normally treated as anempirical coefficient assumed to be dependent either on grain size d (Anderson & Haff, 1988; Doorschot &

Lehning, 2002) or on friction velocity u*¼ffiffiffiffiffiffiffiffiffiffiffiτs=ρa

p(where ρa is the air density) (Shao & Li, 1999). Actually,

equation 2 is widely accepted and applied in aeolian research, but the variable τs is generally considered astime‐averaged value (Anderson & Haff, 1988; Bagnold, 1941; Shao, 2008).

It is noteworthy that equations 1 and 2 are only tenable when τs > τt (elsewise, F = 0). But the surface shearstress in the turbulent boundary layer is always fluctuating (Örlü & Schlatter, 2011) and instantaneousvalues below the threshold τt commonly exist, which requires a strict premise for the application of time‐averaged values in equation 2(i.e., all instantaneous shear stresses are required to be larger than τt). Onthe other side, it is really hard to confirm the aerodynamic threshold τt in an experiment, due to the difficultyto simultaneously measure the instantaneous surface shear stress and aerodynamic entrainment. Over thelast decades, the incipient motion of surface particles has been extensively studied (Lu et al., 2005) andthe mean surface shear stress corresponding to the minimal amount of particle entrainment causing a gen-eral particle motion in an experiment is treated as threshold (Bagnold, 1941, for distinction, labeled incipientthreshold). This incipient threshold only requires that the maximal instantaneous shear stress overcomes thecritical value (aerodynamic threshold, τt) but is not exactly equivalent to τt as defined in equation 2.Moreover, some recent studies suggest that, in the stationary state of saltation, the mean surface shear stressis lower than the aerodynamic threshold (Kok et al., 2012; Walter et al., 2014). This is considered to be themain evidence for the assumption that aerodynamic entrainment is negligible in the stationary state of salta-tion. The effect of surface shear stress fluctuations stemming from turbulence and the complexity of thegranular surface have been neglected in theories for wind‐blown sand, although they are considered innumerous studies on sediment transport (Diplas et al., 2008; Parker et al., 2003; Seminara et al., 2002;Valyrakis et al., 2010, 2013). For a full understanding of aeolian grain transport it seems therefore necessaryto explore turbulent aerodynamic entrainment in more detail.

2. Materials and Methods2.1. Experimental Setup

The experiments were carried out in the wind tunnel of Lanzhou University. The wind tunnel has a worksection of 1.4 m in width, 1.3 m in height, and 20 m in length, and the nominal air velocity can be variedbetween 3 and 40 m s−1.

Wedges and roughness elements are arranged in the front of the work section to generate a turbulent bound-ary layer (Figure 1). Then sandpaper is placed on the bed surface behind the roughness elements to mimicthe characteristics of desert surface, as well as avoid occasional saltation due to detached grains. A metallictray, filled with grains, is mounted flush with the ground downstream of the sandpaper to estimate theentrainment rate F. To estimate F as accurately as possible, the length of the tray in wind direction shouldbe short enough to avoid saltation impact but long enough to neglect influences from the tray's wall. Wemade several tests and found that a tray of width = 285 mm and length = 150 mm satisfies bothrequirements above.

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According to the definition of entrainment rate F in equation 2, Δm is measured as the mass loss of the trayfilled with grains, A the area of the tray, and Δt the run time of each test. An electronic balance with 0.01 gaccuracy serves to measure Δm. All of the tests were repeated at least three times.

By considering that the lost particles must escape through the downwind edge of the tray to yield horizontaltransport, we have

Q¼FÄnL (3)

where Q is the integrated horizontal transport flux (kg · m−1 · s−1) and L is the streamwise length of thetray (as illustrated in the dashed box in Figure 1).

For the surface shear stress measurements, Irwin sensors (Irwin, 1981) were used to measure high‐frequencysignals of the surface shear stress on the sandpaper bed in our wind tunnel experiment. The sensors werevalidated on a smooth flat bed in several papers (Walter et al., 2014; Wu & Stathopoulos, 1994), confirmingto be capable of providing a flat frequency response up to 100 Hz. In this work, a Pitot tube (and hot wire as a

standby) was used to calibrate the relation between mean pressure difference δp measured by an Irwin sen-sor and mean surface shear stress τs obtained by wind profiles (Figure S1 in the supporting information).Since a linear calibration relation is found between mean surface shear stress and mean pressure difference(Figure S2) and we apply it for short times of 0.01 s, a time series of surface shear stress of 100 Hz is obtained.

2.2. Materials

We employ spherical alumina grains with three different mean diameters (d= 40, 70, 120 μm) (Figure S3) toreduce the effect of irregular shape. Their density ρp= 3,900 kg m−3. More than five different wind velocitiesare imposed for each grain size.

3. Results3.1. Dependence of Aerodynamic Entrainment Rate on Mean Surface Shear Stress

Well‐controlled wind tunnel experiments were carried out to measure the average aerodynamic entrain-ment rate and the time series of surface shear stress on a rough bed. The results of the aerodynamic entrain-ment rate F and the time‐averaged surface shear stress τs are illustrated in Figure 2. It is clearly seen that alinear law is satisfied when the mean surface shear stress is large (Figure 2a), while it is not valid when τsgoes to smaller values, in which case F (τs) deviates very strongly from the linear law and an exponentiallaw is found (Figure 2b). By considering the essential mechanism of aerodynamic entrainment as discussedin equations 1 and 2, we deduce the reason for this observation as: If all (at least most) instantaneous surfacestresses exceed the aerodynamic threshold τt to satisfy the requirement of equation 2, the linear law is ten-able; else if a considerable amount of instantaneous surface stress below τt, whether the mean surface shearstress τs is bigger or smaller than τt, the linear law fails and an exponential law works.

We therefore fit equation 2 to the data of the first case (shown as the solid lines in Figure 2a) and the values ofα and τt are obtained. Meanwhile, an empirical exponential law is employed to describe the remaining data(shown as the dashed lines in Figure 2b),

Figure 1. Illustration of our experiment. The hotwire is only used in wind without particles to calibrate the Irwinsensors.

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F¼F0Äne

γ 1τt− 1τs

� �(4)

where τt has been determined by the linear law. F0 and γ are empirical coefficients. F = F0 when τs¼τt, soF0 should be a function of the standard deviation of surface shear stress when τs¼τt. By fitting the data, wefound F0~d

3, γ~α2~dn, which indicate these coefficients depend on grain shape and turbulent flowproperties.

3.2. Turbulent Effects Lead to Different Aerodynamic Entrainment Regimes

To deeply explore the behavior of aerodynamic entrainment effected by fluctuating surface shear stresscaused by wind turbulence, the data of the time series of surface shear stress and the instantaneous entrain-ment rate calculated by equation 1 (only for τs > τt, and F = 0 for τs ≤ τt, α and τt are same to Figure 2)are analyzed.

For instance, the results of particles with diameter of 120 μm are shown in Figure 3 and three typical windconditions are considered. As shown, the fluctuations always dominate the entrainment. For the case of

Figure 2. Measured entrainment rate F versus mean surface shear stress τs . (a) is illustrated in linear vertical axis toemphasize the linear law and (b) in logarithmic vertical axis to emphasize the exponential law. Black color for particlediameters 40 μm, red for 70 μm, and blue for 120 μm; dots with error bars, for experimental data; solid lines, forequation 2; dashed lines, for equation 4.

Figure 3. Time evolutions of surface shear stress τs (a–c) and entrainment rate F (d–f).

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Figure 3a, the mean surface shear stress τs is much smaller than τt, and the instantaneous τs occasionallyexceeds τt to produce sporadic and weak entrainment (shown as Figure 3d). When the mean surface shearstress gets larger (Figure 3b), both frequency and intensity of aerodynamic entrainment events will increase(Figure 3e), until a value of mean surface shear stress is reached (Figure 3c), above which grains are emittedall the time (Figure 3f). Under this condition, continuous aerodynamic entrainment happens, and the linearrelation is satisfied all the time, which means that the instantaneous surface shear stress can be replaced bythe time averaged surface shear stress to appearing in equation 2. Based on the time series of F, the time‐

averaged aerodynamic entrainment rate F is also calculated and the results are consistent with the mea-sured mean entrainment rate as shown in Figure 2, which indicates that the predicated instantaneousentrainment rates shown in Figure 3 are acceptable and the deduction of the reason behind Figure 2 isreasonable.

According to our understanding of aerodynamic entrainment, several regimes can be distinguished asshown in Figure 4a. The incipient thresholdτi, a minimal mean shear stress corresponding to detectable aero-dynamic entrainment, could be defined to divide aerodynamic entrainment into undetectable entrainmentand detectable entrainment. The continuous threshold τc could be defined as the minimal mean surface stressto satisfy the requirement of equation 2, and the aerodynamic entrainment is consequently split into theintermittent entrainment and the continuous entrainment. The former is affected by plenty of instantaneoussurface shear stresses lower than the aerodynamic threshold and the exponential law works. The regimeabove the continuous threshold satisfies the linear law of equation 2 and all (at least most) of instantaneoussurface shear stresses are above the aerodynamic threshold.

The incipient threshold is important to judge the initial particle motion which may trigger fully developedsaltation transport, and the continuous threshold is pivotal to distinguish the data satisfying the linear lawto estimate the aerodynamic threshold. One must, however, note that, τi and τc are both influenced not onlyby the surface particles but also the fluctuations of surface shear caused by wind turbulence, and thereforecannot be replaced by the aerodynamic threshold to be applied in equation 2. The comparison of measuredthresholds obtained from different experiments (Figure S4) indicates that different definitions for the thresh-old adopted in influential papers may be a potential reason to cause the divergence between aeolian trans-port and fluvial transport (the threshold of aeolian transport normally corresponds to sporadic initialmotion, i.e.,τi; but the one in fluvial work considers a τc corresponding to general motion ofsurface particles).

To take the effect from surface shear fluctuations caused by wind turbulence into account, equation 2 couldbe rewritten as

Figure 4. (a) Regimes of aerodynamic entrainment. Three different thresholds are defined. The incipient threshold isdefined as the minimal mean surface shear stress below which grain entrainment could not be detected. The continuousthreshold corresponds to the minimal mean surface shear stress above which grain entrainment continuously occurs toactivate the linear law. The aerodynamic threshold is theminimal average shear stress required to give rise to themotion ofsurface particles. The value aerodynamic threshold could be obtained by fitting the data of continuous entrainment toequation 2. (b) Predictions of universal model involved the effect of surface shear fluctuation caused by wind turbulence.

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F¼∫∞τt α τs − τtð Þp τsð Þdτs (5)

where p(τs) is the probability distribution of surface shear stress τs. Wefound that p(τs) follows a Gaussian distribution (Figure S5). Figure 4b(solid lines) shows the predictions using equation 5 and α and τt aresame as in Figure 2a. The predictions agree quite well with the experi-mental data in both the intermittent and continuous regimes. We alsonotice some deviations, especially for small grains at low shear stress.

The deviation could be caused by the implicit assumptions of equation 5,that α and τt are considered as constants that only depend on particle size.By considering that the linear law has been validated for continuousentrainment and the value of α is weakly dependent on wind condition,we prefer to ascribe the deviation to the incomplete treatment of τt.Based on the research of Shao who proposed approximate log‐normal dis-tributions for the threshold friction velocity (Shao, 2008), we keep themean value unchanged and introduce the log‐normal distribution of thethreshold (see Figure S6), the predictions exhibit better agreement withthe measurements, as shown in Figure 4b (dashed lines). This implies thatthe threshold distribution may be another factor influencing the entrain-ment of grains, especially the smaller ones.

3.3. Comparison of Horizontal Transport

Clearly, the grains entrained from the surface substantially contribute to the horizontal grain transport. Thestreamwise grain flux due to aerodynamic entrainment is calculated by equation 3, and the results are com-parable to that measured in previous work (Bagnold, 1937) in stationary state saltation (Figure 5).Previously, people believed that impact entrainment dominates and that the contribution of aerodynamicentrainment can be ignored in stationary state saltation. It is generally accepted that for the case of saturatedsaltation in which the wind is weakened by airborne particles and the surface shear stress shifts approxi-mately to 0.64τt (Bagnold, 1937), so that the contribution of aerodynamic entrainment may be limited at avery low level, referring to the green box in Figure 5. However, we should also note that for the case of unsa-turated saltation (wind is not weakened by airborne particles, such as at the onset of saltation), surface shearstress may reach a significant level and aerodynamic entrainment can be an efficient way to directly induce ahorizontal grain transport comparable to the steady and saturated saltation (shown as the dashed red line inFigure 5). By considering that the sand stream in the field is never completely steady and saturated (Pähtz etal., 2020; Stout & Zobeck, 1997), the contribution of aerodynamic entrainment in natural horizontal graintransport should not be ignored.

4. Conclusions

Here a series of wind tunnel experiments were executed to deepen our understanding of aerodynamicentrainment in turbulence. The experimental data show that the prevalent model cannot even qualitativelypredict the aerodynamic entrainment rate.

The conventional linear relationship between entrainment rate F and excess shear stress τs − τtð Þ is onlyconfirmed for continuous flux for sufficiently large surface shear stresses. Additionally, intermittent entrain-ment, which is sensitively affected by wind turbulence, exists and follows an exponential law. A modelincluding the effects of surface shear fluctuations [represented by a distribution p(τs)] is proposed and vali-dated by the experiment. Additionally, the shape of the probability distribution of the threshold [p(τt)] isfound to significantly influence the entrainment of small grains.

We have shown that fluctuations in surface shear caused by turbulence and the variation of the entrainmentthreshold caused by the spatially varying surface condition can both be represented by distribution functionsthat should be introduced into the theoretical modeling to fully describe aerodynamic grain entrainment.The picture that emerged here about the spatiotemporal variability of the grain entrainment process andits consequences on the macroscopic entrainment rate is essential if one wants to improve the precision of

Figure 5. Comparison of horizontal transport Q caused by saltation impact(hollow square dots and dashed line) and aerodynamic entrainment (solidsquare dots and solid line). L is the length of the tray used in ourexperiment and s = ρp/ρa is the density ratio between the particle and theair.

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wind‐blown dust/snow/sand transport prediction and develop more efficient future soil preservationtechniques.

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AcknowledgmentsThis study was supported by theNational Key Research andDevelopment Program of China(2016YFC0500900) and the NationalNatural Science Foundation of China(11602100 and 11172118). All data areavailable in the Dryad DigitalRepository (https://datadryad.org/stash/dataset/doi:10.5061/dryad.79cnp5hs1).